Answer

Verified

381.9k+ views

**Hint:**First we have to define what the terms we need to solve the problem are.

Since the given question is to find the number of ways so we use to formula of the combination;

Combination is the number of ways to arrange or count the given problem.

**Formula used:**

${}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}$

n is the total amount and r is the object that needs to arrange into the different sets.

**Complete step by step answer:**

Since there are three vowels and four consonants in the word ARTICLE; that is AIE are the vowel letters and balance RTCL are the consonants letters; (consonants means non vowel letters in the alphabets)

Since there are three vowels and the number of ways of selecting the three vowels from the two require questions are $3{c_2}$(number of the ways)

So that AIE can be have $^3{c_2}$ways in selecting those two vowels for required question

Hence $^3{c_2} = 3$(three factorial divides two factorial)

Similarly, like same way since there are four consonants and the number of ways of selecting the four consonants from the three require question are $^4{c_3}$(number of the ways)

So that RTCL can be have $^4{c_3}$ ways in selecting those three vowels for required question

Hence $^4{c_3} = 4$(four factorial divides three factorial)

Hence combining the both results into multiplication to find the overall requirement is $4 \times 3 = 12$

**So, the correct answer is “Option A”.**

**Note:**${}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}$can be expressed as $^3{c_2} = \dfrac{{3!}}{{2!}}$

If the question is about the number of arrangements, then we use the formula of permutation which is

${}^n{P_r} = \dfrac{{n!}}{{(n - r)!}}$ and $3{p_3} = 3!$

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Give 10 examples for herbs , shrubs , climbers , creepers

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is BLO What is the full form of BLO class 8 social science CBSE